Atmosphere Models for Earth, Mars, and Titan

Update 4-8-2024:  Should any readers want to learn how to do what I do (estimating performance of launch rockets or other space vehicles),   be aware that I have created a series of short courses in how to go about these analyses,  complete with effective tools for actually carrying it out.  These course materials are available for free from a drop box that can be accessed from the Mars Society’s “New Mars” forums,  located at http://newmars.com/forums/,  in the “Acheron labs” section,  “interplanetary transportation” topic,  and conversation thread titled “orbital mechanics class traditional”.  You may have scroll down past all the “sticky notes”. 

The first posting in that thread has a list of the classes available,  and these go far beyond just the two-body elementary orbital mechanics of ellipses.  There are the empirical corrections for losses to be covered,  approaches to use for estimating entry descent and landing on bodies with atmospheres,  and spreadsheet-based tools for estimating the performance of rocket engines and rocket vehicles.  The same thread has links to all the materials in the drop box. 

The New Mars forums would also welcome your participation.  Send an email to newmarsmember@gmail.com to find out how to join up.

A lot of the same information from those short courses is available scattered among the postings here.  There is a sort of “technical catalog” article that I try to main current.  It is titled “Lists of Some Articles by Topic Area”,  posted 21 October 2021.  There are categories for ramjet and closely-related,  aerothermodynamics and heat transfer,  rocket ballistics and rocket vehicle performance articles (of specific interest here),  asteroid defense articles,  space suits and atmospheres articles,  radiation hazard articles,  pulsejet articles,  articles about ethanol and ethanol blends in vehicles,  automotive care articles,  articles related to cactus eradication,  and articles related to towed decoys.  All of these are things that I really did. 

To access quickly any article on this site,  use the blog archive tool on the left.  All you need is the posting date and the title.  Click on the year,  then click on the month,  then click on the title if need be (such as if multiple articles were posted that month).  Visit the catalog article and just jot down those you want to go see.

Within any article,  you can see the figures enlarged,  by the expedient of just clicking on a figure.  You can scroll through all the figures at greatest resolution in an article that way,  although the figure numbers and titles are lacking.  There is an “X-out” top right that takes you right back to the article itself. 

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Update 6-5-2016:  this is one of the most popular articles on the entire website.  I hope this publicly-available information has proven useful to others.
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These data replace the previous post "Mars Atmosphere Model", dated 6-24-12, just below.

Atmosphere Models for Earth, Mars, and Titan GWJ 6-30-12

After perusing several links on the internet, I settled on a June 2007 paper by C. G. Justus and R. D. Braun (ref. 1), which contained rather realistic “typical” atmosphere data for Earth, Mars, Titan, Venus, and Saturn. For manned landings, Earth, Mars, and Titan are the only destinations of interest that have atmospheres. Justus is involved with the site-tailorable EarthGRAM and MarsGRAM models. On both Earth and Mars, site-specific atmosphere models can vary widely, which is what the –GRAM models calculate. For Titan, the Huygens descent probe data are really all we have.

The cited paper (ref. 1) has near-surface atmospheric composition, average molecular weight, and specific heat ratio data, for each world, reproduced here for the three destinations of interest. The report also gives an indication of atmospheric composition versus altitude for each world. For my purposes here, that devolves to an altitude limit above which the surface composition is no longer at all representative.

There are also recommendations for high-altitude average density criteria at which aero-braking and aero-capture apply. These are 4x10^-7 kg/m^3 and 2x10^-3 kg/m^3, respectively. Aero-braking refers to multi-pass atmospheric drag braking into a desired non-escape orbit, and aero-capture refers to one-pass atmospheric drag braking into a non-escape orbit.

For purposes of estimating when significant heating during entry begins, versus significant simple drag effects, the aero-capture altitude is the better measure. Simple drag effects “begin” closer to the aero-braking altitude cited. This is true for all three worlds covered by this document: Earth, Mars, and Titan. Only the relevant altitudes vary.

Earth

Earth’s atmosphere has been modeled in many different ways, all both site- and season-dependent. Some are well-known. These include the US 1962 standard atmosphere, the extended ICAO standard atmosphere, the US polar and cold atmospheres, and the US tropical and hot atmospheres. Some are not so well-known, such as the Max Ambient In-Flight and Min Ambient In-Flight days, given in older versions of the Pratt and Whitney vest-pocket aeronautical handbook. Only the ICAO model extends to 100-km altitudes. Continuum flow models are pretty much inapplicable above roughly 45 or 46 km, which corresponds to the aero-capture altitude.

The density profile can be approximated between two specific altitudes as a simple exponential model dens(z) = dens(0)*exp(-z/Hd), where z is altitude, dens(0) is a curve fit parameter, and Hd is the density scale height. Average density scale height between those two altitudes is estimated by Hd = (z2 – z1)/ln(dens1/dens2). This is applicable to computations of max-deceleration, max-dynamic pressure, max heat rate flux, and max absorbed integral heat flux, all as functions of ballistic coefficient and entry velocity. Those effects I will explore in another posting.

The version reported here is an abbreviated table from the cited paper, and 6 plots, given as figures 1 through 6 below (at end of this article). They include the temperature profile, the pressure profile, the density profile, the speed-of-sound profile, the scale height profile, and a representation of the abbreviated table of values. It resembles the extended ICAO atmosphere model.

There is also a short table just below representing near-surface composition, properties, and scale height models. I interpolate the aero-brake altitude as 92.66 km, versus the aero-capture altitude as 46.72 km. Pressure data in are missing in the reported table and figure above the altitude at which composition varies significantly from surface values.

Table 1 – Earth Atmospheric Surface Parameters

for surface air composition 78.084% N2, 20.946% O2, Ar 9340 ppm, CO2 350 ppm, Ne 18.18 ppm, He 5.24 ppm, CH4 1.7 ppm, Kr 1.14 ppm, H2 0.55 ppm
usually near 1% water vapor

MW Cp/Cv
28.97 1.4

best fit 0-100 km
d(0)kg/m^3 = 1.226
Hd km = 7.256


Mars

The tables and figures are “representative” of Mars, knowing full well that variations there are more severe than on Earth. The data quoted herein are within about half an order of magnitude correct, versus a few percent for Earth. These data are given in figures 6-12 below, plus the following abbreviated table. I interpolate the aero-braking altitude as 94.55 km (comparable to Earth), and the aero-capture altitude as 23.82 km (much lower than on Earth). Pressure data are missing in the reported table and figure above the altitude at which composition varies significantly from surface values.

Table 2 – Mars Atmospheric Surface Parameters

for surface "air" composition CO2 95.32%, N2 2.7% , Ar 1.6%, O2 0.13%, CO 0.08%, H2O 210 ppm, NO 100 ppm, Ne 2.5 ppm, HDO 0.85 ppm, Kr 0.3 ppm, Xe 0.08 ppm

MW Cp/Cv
43.34 1.33

best fit 25-70 km
d(0)kg/m^3 = 0.03032
Hd km = 8.757


Titan

The tables and figures are based on Huygens descent probe data. They are the best we have. These data are given in figures 13-18 below, plus the following abbreviated table. I interpolate the aero-braking altitude as 637 km, and the aero-capture altitude as 192 km. Titan is unusual in having a far deeper atmosphere, of higher surface pressure and a lot higher density (because it is so cold there), than on Earth.


Table 3 – Titan Atmospheric Surface Parameters

for surface "air" composition N2 97.7%, CH4 2.3%

MW Cp/Cv
27.32 1.4

best fit 130-800 km
d(0)kg/m^3 = 0.1006
Hd km = 48.38


References:

1. “Atmospheric Environments for Entry, Descent, and Landing (EDL)”, C. G. Justus (NASA Marshall) and R. D. Braun (Georgia Tech), June, 2007.
2. “Atmospheric Models for Mars Aerocapture”, C. G. Justus, Aleta Duvall, V. W. Keller, no date except latest cited reference 2005.
3. “Mars Global Atmospheric Reference Model (MarsGRAM 2005) Applications for Mars Science Laboratory Mission Site Selection Processes”, H. L. Justh and C. G. Justus, no date except latest cited reference 2005.





Figure 1 – Abbreviated Earth Atmosphere Table


Figure 2 – Earth Atmosphere Temperature Profile


Figure 3 – Earth Atmosphere Pressure Profile


Figure 4 – Earth Atmosphere Density Profile


Figure 5 – Earth Atmosphere Speed of Sound Profile


Figure 6 – Earth Atmosphere Density Scale Height Profile


Figure 7 – Abbreviated Mars Atmosphere Table


Figure 8 – Mars Atmosphere Temperature Profile


Figure 9 – Mars Atmosphere Pressure Profile


Figure 10 – Mars Atmosphere Density Profile


Figure 11 – Mars Atmosphere Speed of Sound Profile


Figure 12 – Mars Atmosphere Density Scale Height Profile


Figure 13 – Abbreviated Titan Atmosphere Table


Figure 14 – Titan Atmosphere Temperature Profile


Figure 15 – Titan Atmosphere Pressure Profile


Figure 16 – Titan Atmosphere Density Profile


Figure 17 – Titan Atmosphere Speed of Sound Profile


Figure 18 – Titan Atmosphere Density Scale Height Profile